City and the Reds eased to victory in their opening games of the season, while Spurs needed a late brace from Kane to secure all three points against Aston Villa.
And Kane has warned Tottenham must follow their rivals every step of the way this season.
"We kept up with them for a while last year but they blew ahead after January," Kane said.
"We have to make sure we get off to a good start. Liverpool set the standard on Friday night and City before us, so it's important that we stay in touch as long as we can.
"We have full belief that we can go all the way but there's a long road ahead and we've got to be fully focused."